Scattering theory of walking droplets in the presence of obstacles

Posted by on May 22, 2016 in Bibliography, Core Bibliography, Theory Bibliography | 0 comments

Dubertrand, R., Hubert, M., Schlagheck, P., Vandewalle, N., Bastin, T., & Martin, J. (2016). Scattering theory of walking droplets in the presence of obstacles. arXiv preprint arXiv:1605.02370.

We aim to describe a droplet bouncing on a vibrating bath. Due to Faraday instability a surface wave is created at each bounce and serves as a pilot wave of the droplet. This leads to so called walking droplets or walkers. Since the seminal experiment by Couder et al [Phys. Rev. Lett. 97, 154101 (2006)] there have been many attempts to accurately reproduce the experimental results. Here we present a simple and highly versatile model inspired from quantum mechanics. We propose to describe the trajectories of a walker using a Green function approach. The Green function is related to Helmholtz equation with Neumann boundary conditions on the
obstacle(s) and outgoing conditions at infinity. For a single slit geometry our model is exactly solvable and reproduces some general features observed experimentally. It
stands for a promising.

Scattering theory of walking droplets in the presence of obstacles

http://arxiv.org/pdf/1605.02370.pdf

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Displacement of an Electrically Charged Drop on a Vibrating Bath

Posted by on Apr 10, 2016 in Bibliography, Extended Bibliography | 0 comments

Brandenbourger, M., Vandewalle, N., & Dorbolo, S. (2016). Displacement of an Electrically Charged Drop on a Vibrating Bath. Physical review letters, 116(4), 044501.

In this work, the manipulation of an electrically charged droplet bouncing on a vertically vibrated, bath is investigated. When a horizontal, uniform and static electric eld is applied to it, a motion is induced. The droplet is accelerated when the droplet is small. On the other hand, large droplets appear to move with a constant speed that depends linearly on the applied electrical eld. In the latter regime, high speed imaging of one bounce reveals that the droplet experiences an acceleration due to the electrical force during the ight and decelerates to zero when interacting with the surface of the bath. Thus, the droplet moves with a constant average speed on a large time scale. We propose a criterion based on the force necessary to move a charged droplet at the surface of the
bath to discriminate between constant speed and accelerated droplet regimes.

Displacement of an Electrically Charged Drop on a Vibrating Bath

 

http://orbi.ulg.ac.be/bitstream/2268/194253/1/PhysRevLett.116.044501.pdf

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Waveguides for walking droplets

Posted by on Oct 12, 2015 in Bibliography, Core Bibliography | 0 comments

Filoux, B., Hubert, M., Schlagheck, P., & Vandewalle, N. (2015). Waveguides for walking droplets. arXiv preprint arXiv:1507.08228.

When gently placing a droplet onto a vertically vibrated bath, a drop can bounce permanently. Upon increasing the forcing acceleration, the droplet is propelled by the wave it generates and becomes a walker with a well de ned speed. We investigate the con nement of a walker in different rectangular cavities, used as waveguides for the Faraday waves emitted by successive droplet bounces. By studying the walker velocities, we discover that 1d con nement is optimal for narrow channels. We also propose an analogy with waveguide models based on the observation of the Faraday instability within the channels.

http://arxiv.org/pdf/1507.08228.pdf

WAVEGUIDE

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On the analogy of quantum wave-particle duality with bouncing droplets

Posted by on Sep 26, 2015 in Bibliography, Core Bibliography, Theory Bibliography | 0 comments

Richardson, C. D., Schlagheck, P., Martin, J., Vandewalle, N., & Bastin, T. (2014). On the analogy of quantum wave-particle duality with bouncing droplets.arXiv preprint arXiv:1410.1373.

We explore the hydrodynamic analogues of quantum wave-particle duality in the context of a bouncing droplet system which we model in such a way as to promote comparisons to the de Broglie-Bohm interpretation of quantum mechanics. Through numerical means we obtain single-slit dif raction and double-slit interference patterns that strongly resemble those reported in experiment and that re ect a striking resemblance to quantum di raction and interference on a phenomenological level. We, however, identify evident di erences from quantum mechanics which arise from the governing equations at the fundamental level.

http://arxiv.org/pdf/1410.1373.pdf

doubleSlit sinfgleSlit

 

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Strings of droplets propelled by coherent waves

Posted by on Sep 26, 2015 in Bibliography, Core Bibliography | 0 comments

Filoux, B., Hubert, M., & Vandewalle, N. (2015). Strings of droplets propelled by coherent waves. arXiv preprint arXiv:1504.00484.

Bouncing walking droplets possess fascinating properties due to their peculiar wave/particle interaction. In order to study such walkers in a 1d system, we considered the case of a few droplets in an annular cavity. We show that, in this geometry, they spontaneously form a string of synchronized bouncing droplets that share a common coherent wave propelling the group at a speed faster
than single walkers. The formation of this coherent wave and the collective droplet behaviors are captured by a model, which sheds a new light on droplet/wave interactions.

http://arxiv.org/pdf/1504.00484.pdf

strings of droplets

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The role of the droplet deformations in the bouncing droplet dynamics

Posted by on May 22, 2013 in Bibliography, Core Bibliography | 0 comments

Terwagne, D., Ludewig, F., Vandewalle, N., & Dorbolo, S. (2013). The role of the droplet deformations in the bouncing droplet dynamics. Physics of Fluids (1994-present)25(12), 122101.

http://www.grasp.ulg.ac.be/article/2013_terwagne_POF.pdf

 

ArXiv Preprint  :

Terwagne, D., Ludewig, F., Vandewalle, N., & Dorbolo, S. (2013). The role of deformations in the bouncing droplet dynamics. arXiv preprint arXiv:1301.7463.

http://arxiv.org/pdf/1301.7463v1.pdf

 

Editor Postprint :

http://orbi.ulg.ac.be/handle/2268/159838

 

Automatic droplet generator

Period doubling transition of bouncing droplet, bifurcation diagram

Simulation with mass-spring system

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